Satellite a105-s2061 motherboard makes clicking noise without any drives hooked up to it and power supply is plugged into it.

SOURCE: Replacement for toshiba satellite A105-S4244 dvd r/rw drive

Sure--the best one is e-bay!
Whenever I need something like this, I find it on e-bay. But if you really need to contact a company, try Spare Parts Wearhouse at 877-253-8898. National Parts Depot at 800-524-8338 may carry Toshiba parts.
I'd almost bet that the part you need is not made by Toshiba, though. Take it out and when looking for a replacement look for the mfg. name and the model.

SOURCE: My Toshiba Satellite A105 will not turn on.

A clicking sound from the hard drive is a sign of death.
I would try another hard drive and reinstall the O/S

SOURCE: toshiba a105, wont power up, clicking sound

I seem to have the same problem. I have an a105-4134. Ive had since June of 2006 and ive kept it clean and have replaced several components throughout its life.

I was working on it few days ago until it just shut off. Confused, I press the power button thinking maybe the power adapter wasn't plugged all the way in and the battery depleted and it shut off. So now the computer will now power on. It lights up but shuts off within 1 second. Keeps doing this over and over.

My first thought was the dc jack as ive read it is common to be faulty after long use. I ordered a new one and unfortunately it was not the culprit. I then suspected the cheap aftermarket power adapter which replaced the dead oem power adapter. Bought a new one and experienced the exact same symptoms yet again.

Now I'm digging deep removing all components one by one. With each one I remove, I gain a few seconds of time that it will stay on before shutting off on its own. I powered it on with only the motherboard and cpu and it does the same thing.

From the original problem in this post, the cpu and motherboard were swapped out and same symptoms still occurred. This being the case, the only component left undiagnosed is the power board itself.

This is where I noticed that the computer will power up and run on battery power. The adapter plugged in will charge the battery but not power the computer while running. With this discovery it means that it cannot be any of the main components causing the problem.

Back to the power board, an obvious problem area seeing how this is tied in with power components. From the looks of it, it seems like a simple switch board but i may be wrong. My next step is to order a new power board. I will let you all know how it turns out.